Explicit Caplet Implied Volatilities for Quadratic Term-Structure Models

Paper: arXiv 2212.04425

Authors: Matthew Lorig, Natchanon Suaysom

Abstract

We derive an explicit asymptotic approximation for implied volatilities of caplets under the assumption that the short-rate is described by a generic quadratic term-structure model. In addition to providing an asymptotic accuracy result, we perform experiments in order to gauge the numerical accuracy of our approximation.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents strong theoretical and mathematical derivations for asymptotic implied volatility under quadratic term-structure models. However, it focuses primarily on numerical simulation accuracy rather than empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Explicit Caplet Implied Volatility<br/>for Quadratic Term-Structure Models (QTSMs)"] --> B["Inputs: Short-rate model parameters<br/>& Caplet strike/maturity"]
    B --> C["Derive Asymptotic Expansion<br/>for Caplet Pricing"]
    C --> D["Map Price Expansion to Explicit<br/>Implied Volatility Formula"]
    D --> E["Numerical Experiments &<br/>Accuracy Benchmarking"]
    E --> F["Outcomes: High numerical accuracy,<br/>fast computation & analytical tractability"]